System and methods for shearless hologram acquisition

ABSTRACT

Systems and methods for shearless digital hologram acquisition, including an apparatus incorporating an illumination source configured to produce a first beam of light, which is then split by a beamsplitter into a reference beam and an object illumination beam. The reference beam is directed onto a phase-shaping optical element which imparts a phase shift to the reference beam and returns the phase-shifted reference beam on itself to the beamsplitter. The object illumination beam is directed onto an object, and a portion of the beam is reflected back to the beamsplitter, which combines the phase-shifted reference beam and object illumination beam substantially coaxially. The combined beams are passed through a focusing lens which focuses them at a focal plane. A digital recorder is positioned at the focal plane to record the spatially heterodyne hologram formed by the focused phase-shifted reference beam and reflected object illumination beam.

BACKGROUND

1. Field of the Invention

The present invention relates generally to the field of holography. Moreparticularly, the present invention relates to systems and methods forshearless digital hologram acquisition system suitable for use with“white light” (spectrally broadband) or laser illumination, or two-colorillumination. For two-color (more than two colors is also possible)implementations, the two colors may either both be broadband (low orvery low coherence) illumination or laser illumination.

In one implementation, an LED (broadband light source) or laser is usedfor illumination, a diffractive or holographic optical element is usedto create the required phase shift in a reference arm, and the hologramis recorded on a digital camera. In one implementation, advancedalignment and signal processing systems and methods, combined with theshearless geometry, afford a one-dimensional (1-D) FFT (Fast FourierTransform) so that the processing time is substantially diminishedcompared to prior art systems that require a two-dimensional (2-D) FFT.

2. Related Art

Prior methods of heterodyne (spatial carrier frequency) classicalholography and of digital hologram acquisition have required both laser(coherent) illumination and that the reference and object (target) beamsbe combined at some angle (there is a shear between the two beams).Lasers have a number of problems, including high expense and generallyrequiring very extensive safety precautions, which makes them even moreexpensive. Additionally, since lasers have long coherence lengths(compared to broader band illumination sources), small reflections fromoptical surfaces will interfere with and make significant noise in thedigital hologram. Previous methods have also required an angle (shear)between the two beams to create the spatially heterodyne fringe patternthat actually records the hologram. The shear is created by reflectingthe reference beam from a mirror or beamsplitter so that it propagatesat a different angle than the object (target) beam. For common pathsystems, such as a Michelson geometry, or the last leg of a Mach-Zendergeometry to the digital recorder, this means that the beams separatespatially from one another, and in fact makes it impossible to use aMichelson geometry for systems with high magnification-the referencebeam becomes so separated due to the shear that it is either clipped bythe optics, does not overlay the object beam, or both. Even with theshorter common path Mach-Zender layout, shear between the two beamsoften causes problems in achieving adequate overlay of the beams. Forlow-coherence illumination source beams it is substantially impossiblein either geometry to get an exact enough overlay to form fringes withthe prior art sheared systems. Another problem with prior art digitalhologram acquisition systems is that they require a two-dimensional(2-D) FFT (Fourier transform) and inverse FFT to separate the objectwave phase and amplitude from the hologram. The 2-D FFT/inverse FFTrequires large computational power or a long wait. Another considerableproblem with prior art systems is that they have no method for measuringphase changes greater than one wavelength or two-pi radians in ashearless geometry. This is a substantial disadvantage for holographicmetrology.

FIG. 1 shows a prior art digital holography system with a Michelsongeometry, where the shear angle between the two beams is indicated as a.Note that for this particular case, nominally a high-magnification case,the reference and object beams no longer have any overlap, as indicated,and therefore cannot form a hologram.

There is therefore a particular need for systems and methods for 1)recording digital holograms in a shearless geometry, 2) recordingdigital holograms with broadband very short coherence length (bothtransverse and longitudinal) illumination, 3) recording digitalholograms which extend the range of metrology substantially beyond onewavelength and 4) reducing the FFT computational requirements forseparating the object wave phase and amplitude from the hologram.

SUMMARY OF THE INVENTION

This disclosure is directed to systems and methods for shearlesshologram acquisition that solve one or more of the problems discussedabove.

The disclosed systems and methods may provide for single-beam or two (ormore) color operation, and for separation of the object beam phase andamplitude from the hologram. The shearless geometry is highly suited fortwo (or more) color operation with either broadband or laserillumination, and systems and methods are introduced herein to enablethis advanced metrology technique. The multi-color operation withshearless geometry extends the measurement capability of holographicmetrology so that third-dimension measurements can be made withoutambiguity over a much wider range with excellent overlay of the objectand reference beams in Michelson, Mach-Zender, or other geometry in ashearless fashion.

One apparatus for shearless recording of a spatially heterodyne hologramwith broad-band or laser illumination includes: an illumination sourceor sources; a beamsplitter optically coupled to the illuminationsource(s); a reference beam phase-shaping optical element opticallycoupled to the beamsplitter; an object optically coupled to thebeamsplitter; a focusing lens optically coupled to both the referencebeam phase-shaping optical element and the object; and a digitalrecorder optically coupled to the focusing lens. A reference beam isincident upon the phase-shaping optical element, and the reference beamand an object beam are focused by the focusing lens at a focal plane ofthe digital recorder to form a spatially heterodyne hologram.

This system and corresponding methods provide advantages in that theobject and reference beams are unsheared and do not separate from oneanother as they travel a common optical path in space. Additionally,since the beams can be substantially perfectly overlapped with theshearless system and methods, no expensive and potentially dangerouslaser is required for the illumination source, although the system isalso perfectly compatible with laser illumination and also providestremendous advantages for the case of laser illumination.

The systems and methods provide advantages in that computer assistedholographic measurements can be more easily and less expensively madewith higher quality results. Additionally, the advanced systems andmethods allow substantially decreased computation time or computationalpower by allowing the FFT's to be 1-D rather than 2-D, and two-coloroperation with the shearless geometry and 1-D FFT/IFFT provides agreatly expanded measurement range.

One particular embodiment comprises an apparatus to shearlessly record ahologram. The apparatus includes an illumination source configured toproduce a first beam of light. The beam is split by a beamsplitter intoa reference beam and an object illumination beam. The reference beam isdirected onto a phase-shaping optical element which imparts a phaseshift to the reference beam and returns the phase-shifted reference beamon itself to the beamsplitter. That is, the phase-shifted reference beamis returned in the same direction from which the non-phase-shiftedreference beam was received, instead of being returned at an angle withrespect to the received beam. The object illumination beam is directedonto an object, and a portion of the beam is reflected back to thebeamsplitter. The beamsplitter receives the phase-shifted reference beamand object illumination beam and combines them substantially coaxially.The combined beams are passed through a focusing lens which focuses themat a focal plane. A digital recorder is positioned at the focal plane torecord the spatially heterodyne hologram formed by the focusedphase-shifted reference beam and reflected object illumination beam.

The illumination source may, for example, be a laser, light emittingdiode (LED), a spectrally filtered incandescent light source, or an arclamp. The phase-shaping optical element may, e.g., be a diffractiveoptical element with a blaze grating or a holographic optical elementwhich is configured to impose a phase shift, such as a linear phaseshift or repetitively increasing and decreasing phase shift, on thereference beam. The apparatus may include conditioning optics, such as abeam expander or spatial filter, positioned between the illuminationsource and the beamsplitter to optically process the first beam of lightbefore it is received by the beamsplitter. The digital recorder may be aCCD or CMOS camera, and a digital storage medium may be coupled to thedigital recorder to store the hologram data. The beamsplitter, thephase-shaping optical element, and the digital recorder may beconfigured according to various geometries, such as a Michelsongeometry.

Another embodiment comprises a method for shearlessly recording ahologram. In this method, a beam of light is first provided. The beam issplit into a reference beam and an object illumination beam. A phaseshift is imparted to the reference beam, and an object is illuminatedwith the object illumination beam. The phase-shifted reference beam anda portion of the object illumination beam reflected from the object arethen combined in a substantially coaxial manner. The phase-shiftedreference beam and reflected object illumination beam are then focusedat a focal plane, forming a spatially heterodyne hologram.

Numerous other embodiments are also possible.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages of the invention may become apparent uponreading the following detailed description and upon reference to theaccompanying drawings.

FIG. 1 illustrates a schematic of a prior art high-magnificationMichelson system indicating that shear has caused the reference andobject beams to no longer overlap.

FIG. 2 shows a schematic of a particular embodiment of the presentinvention using Michelson Geometry, illustrating unsheared beams withdiffractive or holographic Phase-Shaping Element in the Reference Arm.

FIG. 3 illustrates a schematic of a Two-Color Digital Holography Systemwith shearless geometry suitable for 1-D FFT analysis.

FIG. 4 shows an Example of Carrier Frequency Fringes suitable forseparation of Object Waves using Two-Color Digital Holography. Whileorthogonal carrier frequencies in real and Fourier space areadvantageous, all that is required for a 1-D FFT is the ability tomathematically rotate an axis perpendicular to the carrier frequency ofinterest.

FIG. 5 depicts an example of a spectrally broadband illuminationholography system with closely matched Reference and Object beam pathlengths and reticle alignment target to allow precision overlay of therecombined beams at the digital camera.

While the invention is subject to various modifications and alternativeforms, specific embodiments thereof are shown by way of example in thedrawings and the accompanying detailed description. It should beunderstood, however, that the drawings and detailed description are notintended to limit the invention to the particular embodiment which isdescribed. This disclosure is instead intended to cover allmodifications, equivalents and alternatives falling within the scope ofthe present invention as defined by the appended claims.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

One or more embodiments of the invention are described below. It shouldbe noted that these and any other embodiments described below areexemplary and are intended to be illustrative of the invention ratherthan limiting. Descriptions of well-known components and processingtechniques are omitted so as to not unnecessarily obscure the presentinvention in detail.

As described herein, various embodiments of the invention comprisesystems and methods for shearless hologram acquisition. Significantfeatures of an apparatus for shearless digital hologram acquisitioninclude the use of a phase-shaping optical element in the reference arm;using a broad-band illumination source with the optical paths, bothlongitudinal and transverse, matched to better than the longitudinal andtransverse coherence lengths; arranging the system so that two (or more)colors can be used to record simultaneous holograms on the same digitalcamera exposure, or sequentially recording two (or more) colors on thesame exposure by offsetting the direction of the carrier fringerecordation between the two (or more) colors; and building and aligningthe system, or rotating the coordinate axes, so that the spatiallyheterodyne carrier frequency fringes are substantially aligned alongeither the x-axis or y-axis (or one color on the x-axis and one color onthe y-axis for two-color recordation) of the system so that a 1-D FFTcan be used rather than a 2-D FFT. The alignment can be replaced by axisrotations which make one axis of the coordinate system perpendicular tothe carrier-frequency fringes of the object wave to be recovered fromthe hologram.

The systems and methods for advanced digital holography disclosed hereinallow for the use of simpler optical systems, for the use of lessexpensive apparatus, for improved quality of digital hologramacquisition, and for improved methods of analysis of the hologram fordetermining the amplitude and phase of the original object wave at everyrecorded pixel. By contrast, the prior art does not describe any methodfor shearlessly forming a heterodyne (spatial carrier frequency)hologram. Shearless formation allows the use of the simpler Michelsongeometry even in high magnification applications, and also remains anadvantage for beam overlay even using the more complex Mach-Zendergeometry. Neither does the prior art teach how to use broadband lightfor recordation of holograms, how to simultaneously or sequentiallyrecord holograms with two (or more) colors (either broadband or laserillumination) in a shearless geometry on the same digital cameraexposure, or how to analyze the hologram for the original object wavephase and amplitude using only a one-dimensional (and therefore muchfaster) Fourier transform and inverse Fourier transform.

System Overview

Shear between the reference and object beam makes it impossible for theprevious embodiments of digital holography to use a Michelson geometryat high magnifications, and prevents good overlay of the two beams(which is necessary for creation of fringes with broadband illumination)even in a Mach-Zender geometry. This problem is overcome by introducinga phase-shaping optical element (which can be a diffraction grating,holographic element, birefringent optical element, wedged glass, orother phase-modifying element), which modifies the phase of thewavefront without requiring reflection of the wave at a non-normalangle. Thus, after recombination, both the reference and object/targetbeams travel the optical path at substantially the same angle and can beoverlaid substantially exactly on one another.

Additionally, prior-art embodiments of digital holography have notprovided a shearless method for removing the ambiguity in phasemeasurements where the resolution-element-to-resolution-elementdifference in phase is greater than one wavelength. This problem isovercome by providing illumination at two or more different wavelengthsor bands of wavelengths (“colors”) with a phase-shaping optical elementfor each color in the reference arm, and simultaneously or sequentiallyrecording the digital hologram on the same exposure of the recordationdevice at two (or more) wavelengths where the required spatialcarrier-frequency fringes are created by the phase shaping opticalelements, rather than combining the beams at an angle. Use of thephase-shaping optical element allows the two beams to be combined in aco-linear fashion so that they can be exactly overlaid and formsatisfactory carrier-frequency fringes even with low-coherence orspectrally broadband illumination.

Additionally, this shearless method of forming the holograms greatlysimplifies proper illumination of the recordation device with the bestoptical quality of each of the individual beams. In sheared geometries,it is often very difficult to properly illuminate the recordation devicewith both beams since the shear causes them to spatially separate. Inorder to separate the two unsheared holograms in Fourier-space (after anFFT), the fringes created in real space by the phase-shaping opticalelement for one of the colors are created with a significantly differentx and y component of the carrier frequency, compared to the spatialcarrier frequency fringes created by the other color, so that when the1-D FFT is performed, the holograms are substantially separated from oneanother in Fourier space, and the object waves can therefore bereproduced without any interference or cross-talk between the colors. Ingeneral, one of the carrier frequencies will have a much higherx-component frequency and the other carrier frequency will have a muchhigher y-component frequency, thus allowing separation of the objectwaves in Fourier space.

Aligning the carrier-frequency fringes of a single-color (for eitherbroadband or laser illumination) hologram substantially parallel toeither the x or y-axis allows a 1-D FFT to be used without axis rotationto retrieve the object beam phase and amplitude from the complexhologram by performing a 1-D FFT on the axis perpendicular to thefringes, translating the zero-frequency (0) axis location to the carrierfrequency location, filtering around the new axis, and performing aninverse 1-D FFT. For two-color digital holography, if the fringes forone color are parallel to the x-axis and the fringes for the secondcolor are parallel to the y-axis, then a 1-D FFT along the x-axis,axis-translation to the carrier frequency, filtering operation, and 1-Dinverse FFT can be used to recreate the phase and amplitude of thesecond color object wave, and a 1-D FFT along the y-axis, axistranslation, filtering operation, and 1-D inverse FFT can be used torecreate the phase and amplitude of the first color object wave.Similarly, rather than aligning the fringes parallel to either thex-axis or y-axis, it is possible to perform a mathematical coordinaterotation so that one of the axes is perpendicular to thecarrier-frequency fringes. The axis rotation method of alignment of acoordinate axis to one set of carrier frequency fringes is in generaluseful when more than two holograms are recorded on the same digitalrecordation device, or when mechanically aligning the system (so thatthe fringes are created parallel to one of the system axes) is notconvenient. This is another variation which allows use of the 1-D FFTrather than the 2-D FFT. More generally, a coordinate rotation allowsuse of the 1-D implementation even when the carrier frequencies cannotbe made exactly orthogonal in real-space or Fourier space. The onlyrequirement is that the difference in frequency components between thecarrier frequencies is large enough that the undesired carrier frequencyshows up as a substantially different frequency in the FFT transform ofthe. other carrier.

Note that, if desired, the methods described above can also be used forillumination sources of the same wavelength to either simultaneously orsequentially expose a single frame of the digital recordation device,thus allowing differential measurements of the target in the shearlessgeometry.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Shearless Digital Holography System

Referring now to FIG. 2, a specific embodiment of a shearlessholographic system is depicted. Light from an illumination source 210passes through conditioning optics 220, which may (or may not) includecollimation, filtering, diffusion, or other optical conditioning of thelight from the illumination source. The beam from illumination source210 is split by a beamsplitter 230 into object and reference beams. Theobject beam strikes the target object 240 and returns through thebeamsplitter 230, while the reference beam is returned on itself by aphase-shaping optical element 250 (i.e., the returned beam issubstantially coaxial with the original reference beam.) Thephase-shifted reference beam is recombined with the object beam at thebeamsplitter 230. The combined beams (the phase-shifted reference beamand the returned object beam) are substantially co-linear and overlaid.A focusing lens 260 then focuses both beams simultaneously onto therecording array plane of a digital camera 270, where the hologram andits spatial carrier frequency fringes created by the phase shift fromthe phase shaping optical element are recorded.

Examples of phase-shaping optical elements include: a holographicoptical element formed by interfering counter-propagating co-linearwaves where the hologram recording material is at an angle to the twobeams; a blaze grating used in the −1 (minus one) order; a glass wedgefollowed by a mirror perpendicular to the beam path; a linearlyincreasing and decreasing glass wedge (the wedge reverses slope in aperiodic fashion so that the average glass thickness is constant whenaveraged over a complete period for the wedge).

Two-Color Digital Holography System

Referring now to FIG. 3, a specific embodiment of a two-color digitalhologram acquisition system is depicted. This method is not limited tojust two colors. Colors may be added to the system as long as thespatial carrier frequencies are arranged so that the object wavefrequencies do not overlap in Fourier space. In this embodiment, lightfrom two illumination sources (310, 315) is combined by a dichroicmirror 320 (which could also be a simple beamsplitter or other form ofbeam combiner). The light from the illumination sources then passesthrough conditioning optics 330, which may (or may not) includecollimation, filtering, diffusion, or other optical conditioning of theillumination sources.

The substantially co-linear illumination beams (of both colors) are thensplit by a beamsplitter 340 into object and reference beams. The objectbeam strikes the target object 350 and returns through the beamsplitter340, while the reference beam is split into both of its colors by adichroic mirror 325 or some other type of splitting element. Eachindividual color reference beam is returned on itself by a phase-shapingoptical element (360, 365), and the dichroic mirror 325 recombines thephase-shifted reference beams. Then, the combined reference beam isitself recombined with the object beam by the beamsplitter 340. For thecase where the phase-shaping optical element returns the beamssubstantially on themselves, the reference and object beams will besubstantially co-linear and overlaid on one another after recombination.A focusing lens 370 then focuses both beams simultaneously onto therecording array plane of a digital camera 380, which records thehologram and the spatial carrier frequency fringes created by the phaseshift from the phase shaping optical element.

In order for the phase and amplitude of each color object beam to beindividually separable from the other beams in Fourier space, thecarrier frequency fringes in the camera recordation plane must becreated at substantially different frequency components. FIGS. 4A-4Dshow an example where the carrier frequency fringes of Color 1 areperpendicular to the carrier frequency fringes of Color 2. It should benoted that the subject matter of the figures (e.g., carrier frequencyfringes) comprise variations in intensity that are normally depicted byshades of gray. The figures are black and white representations of thesubject matter, which is sufficient for the purposes of the followingdescription. For example, FIG. 4A is presented for the purposes ofillustrating the horizontal fringes formed by Color 1. Similarly, FIGS.4B and 4C are presented to illustrate the vertical fringes formed byColor 2, and the combined fringes of both colors, respectively. FIG. 4Dis presented to illustrate the 2-D FFT of the 2-color hologram in FIG.4C.

FIG. 4A illustrates the carrier frequency fringes achieved by arrangingthe Phase Shaping Optical Element (which could also be a mirror sincethis method is also compatible with sheared holography) for Color 1, sothat a linear vertical phase shift is created, resulting in horizontalfringes. FIG. 4B illustrates the carrier frequency fringes achieved byarranging the Phase Shaping Optical Element for Color 2 so that a linearhorizontal phase shift is created, resulting in vertical fringes. FIG.4C illustrates the simultaneous exposure of the digital camera to bothfringe patterns. Finally, FIG. 4D shows the FFT of the image in FIG. 4C.Note that when the FFT is taken, the frequency component separation in xand y of the spatial carrier frequency fringe patterns from the twocolors results in a total separation of the data in FFT space. Thecircles drawn on the figure indicate the separated sidebands for Color 1and for Color 2.

While a 2-D FFT is used to illustrate the separation of the beams inFourier space, only a 1-D FFT and Inverse Fast Fourier Transform (IFFT)are required to recover each of the Object Beams. Thus, a 1-D FFTperpendicular to the spatial carrier frequency fringes, translation ofaxes to the carrier frequency for Color 1, filtering operation, and aninverse FFT results in the phase and amplitude of the Object Wave forColor 1 only. A similar procedure results in recovery of the phase andamplitude of the Object Wave for Color 2 only.

Note that it is not necessary to use a 90-degree angle as the anglebetween the fringes of Color 1 and Color 2. Other angles are entirelypossible, but the advantage of using the 90-degree angle is that no axisrotation is required if the two carrier frequency fringe sets areparallel to the x and y axes. A 1-D FFT and IFFT can be used to recoverthe phase and amplitude of the object waves even for the case where thetwo sets of carrier frequency fringes are not orthogonal. In this case,an axis rotation must be carried out so that one of the axes isperpendicular to the carrier frequency under consideration. A 1-D FFTcan then be carried out along this axis and the zero frequency locationtranslated to the carrier frequency, the result filtered to only includethe object beam frequencies under consideration, and then an inverse FFTproduces the phase and amplitude of only that object wave. In the casewhere neither carrier frequency for either of the two colors is parallelto an axis, an axis rotation must be performed for each color to alignone axis perpendicular to the carrier fringes for that color. Followingthis by a 1-D FFT, translation, filtering, and IFFT for each respectivecolor returns the phase and amplitude of each of the respective colors.

Once the complex Object Waves for Color 1 and Color 2 are recovered asdescribed above, then without any further processing (other thanpossible coordinate rotations if necessary to place them both in thesame coordinate system,) one of the Object Waves is divided by the otherObject wave, corresponding pixel by corresponding pixel (e.g., thecomplex value of the Object Wave for Color 1 at pixel (1,1) is dividedby the complex value of the Object Wave for Color 2 at pixel (1,1)).Since there is an average wavelength difference between the two colors,the resulting phase value created by dividing the two complex objectwaves by one another unambiguously extends the phase measurement rangeof the system. For instance, if there is a 10% difference in wavelengthsbetween the two colors, then the phase measurement range over whichphase is unambiguously measured is extended to 10 wavelengths (averagewavelength divided by the difference between the two measurementwavelengths times the wavelength). This feature thus tremendouslyextends the usefulness of digital holographic measurements and makes itavailable in the very advantageous shearless geometry with only a 1-DFFT required.

One-Dimensional FFT for Object Wave Recovery

The use of a one-dimensional FFT for recovery of the Object Wave isillustrated by examining just one of the colors illustrated in FIG. 4.For instance, if the Phase-Shifting Optical Element is arranged so thata linear vertical phase shift is induced, as illustrated by thehorizontal fringes in FIG. 4A, then only a 1-D FFT in the y-direction(vertical axis) is required to recover the object wave phase andamplitude. A one-dimensional FFT in the y-direction, followed by an axistranslation to the carrier frequency, followed by a filtering operation,followed by a 1-D IFFT, extracts the phase and amplitude of the objectwave only, using just a 1-D FFT and IFFT, not the 2-D FFT and IFFTrequired by all prior art. Note that the digital Fourier transforms neednot be FFT and IFFT, many other digital Fourier transforms besides theFast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT)will also work.

Use of Broadband Illumination for Digital Hologram Acquisition

It has been generally accepted that only highly coherent (laser) sourcesare suitable for holography, and digital holography has only beenproposed using such sources in the prior art. In fact, althoughholography was invented in 1949, it languished on the shelf until theinvention of lasers, followed by the invention of spatially heterodyneholography by Leith and Upatnieks. However, the use of laserillumination is not strictly required, and broadband (“white light”)illumination can be advantageous in many situations. In particular, nothaving laser illumination can greatly reduce the cost and complexity ofa digital holography system, since many lasers are very expensive andrequire considerable safety precautions to prevent injury to users orbystanders.

For systems that require extremely low noise, broadband illumination isalso an advantage. In highly coherent systems, extraneous reflectionsfrom lens surfaces that reach the recording camera interfere coherentlywith the designed reference and object beams, creating noise in thecarrier fringes. With broadband illumination, the reflections from thelenses have traveled a distance different by more than the coherencelength from the path traveled by the designed beams, and thereforecannot interfere coherently with the reference and object beams. Thecarrier frequency fringe noise is thereby tremendously reduced.

FIG. 5 provides an example of a system using broadband illumination. Inthis system, light is provided by an illumination source 510, which inone embodiment may be a green LED. Light from illumination source 510passes through conditioning optics 320, which may, as noted above,perform collimation, filtering, diffusion, or other optical conditioningof the light. In this embodiment, the light from illumination source 310is also passed through a reticle 530 and a lens 540. The light beam isthen split by a beamsplitter 550 into object and reference beams. Inthis embodiment, beamsplitter 550 is a split prism. The object beamstrikes the target object 560 and returns through beamsplitter 550,while the reference beam is returned on itself by a phase-shapingoptical element 570. The phase-shifted reference beam is recombined withthe object beam at the beamsplitter 550 so that they are substantiallyco-linear and overlaid. A focusing lens 580 then focuses both beamssimultaneously onto the recording array plane of a digital camera 590,where the hologram and its spatial carrier frequency fringes created bythe phase shift from the phase shaping optical element are recorded.

In order to use broadband illumination, the path lengths for thereference and object beams must be very carefully matched, to adifference less than the longitudinal coherence length of theillumination:δl<λ ²/δλ,where δl is the path length difference between the reference and objectpaths, λ is the average wavelength of the illumination source, and δλ isthe spectral bandwidth of the illumination source. As an example, forillumination with a green LED of wavelength 530 nm and spectralbandwidth of 5 nm, the path lengths of the reference and object beamsmust be matched to better than ˜56 microns. This is easily achievable byclosely matching the design pathlengths and then providing apiezoelectrically driven longitudinal motion for the phase-matchingoptical element. Such piezoelectric stages can have motion resolution of10 nm or less. Many other methods of precisely matching the path lengthsare also available.

Additionally, the object and reference beams must be exactly matched toone another in the transverse dimension, much more exactly than in anyprior art implementation. The two beams must be recombined so that theexact areas that were split apart are joined back together to anaccuracy better than the transverse coherence length (Born & Wolf,Seventh (expanded) Edition, p. 575, replace ρ, the source size, by Rδθwhere R is the distance from the beamsplitter to the recombinationplane):δr<(Kλ _(avg))/(δθ),where δr is the allowable mismatch in overlay of the beams, K is aconstant equal to 0.61 for no fringe contrast and smaller for goodcontrast, λ_(avg) is the average wavelength of the broadbandillumination source, and δθ is the divergence angle of the illuminationsource in radians. For instance, if the illumination source is a greenLED with average wavelength of 530 nm, spectral bandwidth of 5 nm, anddivergence angle after collimation of seven degrees, then the allowableerror in overlay of the two beams is ˜6.5 microns if we use K=0.3 (˜33%spatial carrier frequency fringe contrast). Overlay of the two beams canbe facilitated by passing the illumination beam through an alignmentreticle 530 before splitting the beam, and arranging the optics suchthat the alignment reticle is also in focus at the digital recordingplane. Clearly, in order to achieve this kind of overlay excellentoptics and alignment must be used, but this is well within the actualstate of the art.

Flat-Field Correction

The optical errors inherent in the system may be substantially removedby the method of flat-field correction. To make a flat field correctionfor reflection holography, the target is replaced by a flat referencesurface which returns a plane wave. For a transmissive holographysystem, the object is simply removed from the system. A hologram isformed with the “perfect” target or with the target removed. The objectwave from the “flat-field hologram” (reference hologram) is separatedfrom the reference hologram by the standard methods of Fouriertransform, axis translation, filtering, and Inverse Fourier transform.When a hologram is made of an object (target) to be analyzed, thecomplex object wave from the object under investigation may be dividedby the complex object wave from the flat-field/reference hologram, andthe optical wavefront errors and systematic noise are substantiallyremoved from the measurement, greatly improving the accuracy ofrecreation of the object wave from the object/target underinvestigation.

Advantages

A shearless digital hologram acquisition system representing oneembodiment of the invention is cost effective and advantageous for atleast the following reasons. The shearless geometry allows a simplerMichelson geometry to be used for systems with arbitrary magnification,which is impossible with a sheared system, since the beams cease tooverlap with one another (and therefore no hologram is created) for manyimplementations of the Michelson geometry. Even with a Mach-Zendergeometry, the shear between the beams makes it difficult to adequatelyoverlap the beams in many instances, and impossible for low coherencesystems. For low coherence systems, the shearless geometry is arequirement, since it is otherwise impossible to overlap the beams sothat they will interfere with one another-very low coherenceillumination requires that the equivalent portions of the two beamsoverlap one another exactly. Use of the 1-D FFT, which is achieved byarranging the phase-shaping optical element so that the induced phaseshift creates fringes parallel to either the x-axis or y-axis of thesystem or by rotating the coordinate system to have one axisperpendicular to the carrier frequency fringes, allows for substantiallyfaster or less expensive (lower computational power) analysis of theholograms for separation of the object wave phase and amplitude from theraw spatially heterodyne hologram carrier frequency fringes.

There are many variations of the embodiments described above which arewithin the scope of the present disclosure and the appended claims.These variations may include, for example, the elimination of thefocusing lens (e.g., 260,) which is used to eliminate the effects ofdiffraction. This may not be necessary for testing very flat opticalsurfaces, so the lens may not be used in some embodiments. In anotheralternative embodiment, the system may be configured so that the objectillumination beam is passed through the target object, rather than beingreflected from it. In an alternative embodiment of a multi-color system,the holograms of the different colors could be recorded by the recordingdevice on separate frames, rather than a single frame. In anotheralternative embodiment, digital Fourier transforms or other kinds offrequency transforms could be used instead of the FFT's described above.

The benefits and advantages which may be provided by the presentinvention have been described above with regard to specific embodiments.These benefits and advantages, and any elements or limitations that maycause them to occur or to become more pronounced are not to be construedas critical, required, or essential features of any or all of theclaims. As used herein, the terms “comprises,” “comprising,” or anyother variations thereof, are intended to be interpreted asnon-exclusively including the elements or limitations which follow thoseterms. Accordingly, a system, method, or other embodiment that comprisesa set of elements is not limited to only those elements, and may includeother elements not expressly listed or inherent to the claimedembodiment.

While the present invention has been described with reference toparticular embodiments, it should be understood that the embodiments areillustrative and that the scope of the invention is not limited to theseembodiments. Many variations, modifications, additions and improvementsto the embodiments described above are possible. It is contemplated thatthese variations, modifications, additions and improvements fall withinthe scope of the invention as detailed within the following claims.

1. An apparatus to shearlessly record a hologram comprising: anillumination source configured to produce a first beam of light; abeamsplitter configured to split the first beam into a reference beamand an object illumination beam; a phase-shaping optical elementconfigured to impart a phase shift to the reference beam and to returnthe phase-shifted reference beam to the beamsplitter substantiallycoaxially with the non-phase-shifted reference beam; wherein thebeamsplitter is configured to receive the phase-shifted reference beamand a portion of the object illumination beam which is reflected from anobject and to substantially coaxially combine the phase-shiftedreference beam and the reflected portion of the object illuminationbeam; a focusing lens configured to receive the combined phase-shiftedreference beam and reflected object illumination beam and to focus thecombined phase-shifted reference beam and reflected object illuminationbeam at a focal plane; and a digital recorder positioned at the focalplane and configured to record a spatially heterodyne hologram formed bythe focused phase-shifted reference beam and reflected objectillumination beam.
 2. The apparatus of claim 1, wherein the digitalrecorder comprises a device selected from the group consisting of a CCDcamera and a CMOS camera.
 3. The apparatus of claim 1, furthercomprising conditioning optics positioned between the illuminationsource and the beamsplitter and configured to optically process thefirst beam of light before the first beam is received by thebeamsplitter.
 4. The apparatus of claim 3, wherein the conditioningoptics comprise a beam expander.
 5. The apparatus of claim 3, whereinthe conditioning optics comprise a spatial filter.
 6. The apparatus ofclaim 1, wherein the beamsplitter, the phase-shaping optical element,and the digital recorder are configured according to a Michelsongeometry.
 7. The apparatus of claim 1, further comprising a digitalstorage medium coupled to the digital recorder and configured to storethe spatially heterodyne hologram.
 8. The apparatus of claim 1, whereinthe illumination source comprises a laser.
 9. The apparatus of claim 1,wherein the illumination source comprises a light emitting diode (LED).10. The apparatus of claim 1, wherein the illumination source comprisesa spectrally filtered incandescent light source.
 11. The apparatus ofclaim 1, wherein the illumination source comprises an arc lamp
 12. Theapparatus of claim 1, wherein the phase-shaping optical elementcomprises a holographic optical element which is configured to generatethe phase-shifted reference beam by imposing a linear phase shift on thenon-phase-shifted reference beam.
 13. The apparatus of claim 1, whereinthe phase-shaping optical element comprises a diffractive opticalelement with a blaze grating.
 14. The apparatus of claim 1, wherein thephase-shaping optical element comprises a holographic optical elementwhich is configured to generate the phase-shifted reference beam byimposing a repetitively increasing and decreasing phase shift on thenon-phase-shifted reference beam.
 15. The apparatus of claim 1, whereinthe beamsplitter comprises a plate beamsplitter.
 16. The apparatus ofclaim 1, wherein the beamsplitter comprises a cube beamsplitter.
 17. Amethod for shearlessly recording a hologram comprising: providing afirst beam of light; splitting the first beam into a reference beam andan object illumination beam; imparting a phase shift to the referencebeam; illuminating an object with the object illumination beam;substantially coaxially combining the phase-shifted reference beam and aportion of the object illumination beam reflected from the object;focusing the phase-shifted reference beam and reflected objectillumination beam at a focal plane; and recording a spatially heterodynehologram formed at the focal plane by the focused phase-shiftedreference beam and reflected object illumination beam.
 18. The method ofclaim 17, further comprising optically conditioning the first beam oflight.
 19. The method of claim 18, wherein optically conditioning thefirst beam of light comprises spatially filtering the first beam oflight.
 20. The method of claim 17, wherein imparting a phase shift tothe reference beam comprises reflecting the reference beam off aholographic optical element which is configured to impose phase shift onthe reference beam.